Dynamics of Structures

ISBN-10: 9058092461
ISBN-13: 9789058092465
Edition: 2nd 2002 (Revised)
Authors: J. L. Humar
List price: $199.95
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Description: A comprehensive coverage of the analytical methods of dynamic analysis. Topics include: Formulation of the equations of motion using the principles of both vector mechanics and analytical mechanics; Free vibration response; Determination of  More...

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Book details

List price: $199.95
Edition: 2nd
Copyright year: 2002
Publisher: CRC Press LLC
Publication date: 4/15/2002
Binding: Paperback
Pages: 996
Size: 6.75" wide x 9.75" long x 2.25" tall
Weight: 4.048
Language: English

A comprehensive coverage of the analytical methods of dynamic analysis. Topics include: Formulation of the equations of motion using the principles of both vector mechanics and analytical mechanics; Free vibration response; Determination of frequencies and mode shapes; Forced vibration response; Numerical integration of the equations of motion; Frequency domain analysis; Analysis of continuous systems; and Wave propagation analysis.A unique feature of the text is its recognition of the impact of digital computers on the analysis of dynamic response. The book give special emphasis to discrete methods and provides a comprehensive coverage of both the traditional and the state of the art numerical techniques of response analysis, such as analysis by numerical integration of the equations of motion and analysis through frequency domains. A healthy array of examples and exercise problems mark the author's commitment to clarity and reader comprehension.This revised and updated edition includes coverage of the new developments in dynamic analysis, as well as additional practice problems.

Preface
List of Symbols
Introduction
Objectives of the study of structural dynamics
Importance of vibration analysis
Nature of exciting forces
Mathematical modeling of dynamic systems
Systems of units
Organization of the text
Formulation of the Equations of Motion: Single-Degree-of-Freedom Systems
Introduction
Inertia forces
Resultants of inertia forces on a rigid body
Spring forces
Damping forces
Principle of virtual displacement
Formulation of the equations of motion
Modeling of multi-degree-of-freedom discrete parameter system
Effect of gravity load
Axial force effect
Effect of support motion
Formulation of the Equations of Motion: Multi-Degree-of-Freedom Systems
Introduction
Principal forces in multi-degree-of-freedom dynamic system
Formulation of the equations of motion
Transformation of coordinates
Finite element method
Finite element formulation of the flexural vibrations of a beam
Static condensation of stiffness matrix
Application of the Ritz method to discrete systems
Principles of Analytical Mechanics
Introduction
Generalized coordinates
Constraints
Virtual work
Generalized forces
Conservative forces and potential energy
Work function
Lagrangian multipliers
Virtual work equation for dynamical systems
Hamilton's equation
Lagrange's equation
Constraint conditions and lagrangian multipliers
Lagrange's equations for discrete multi-degree-of-freedom systems
Rayleigh's dissipation function
Free Vibration Response: Single-Degree-of-Freedom System
Introduction
Undamped free vibration
Free vibrations with viscous damping
Damped free vibration with hysteretic damping
Damped free vibration with Coulomb damping
Forced Harmonic Vibrations: Single-Degree-of-Freedom System
Introduction
Procedures for the solution of the forced vibration equation
Undamped harmonic vibration
Resonant response of an undamped system
Damped harmonic vibration
Complex frequency response
Resonant response of a damped system
Rotating unbalanced force
Transmitted motion due to support movement
Transmissibility and vibration isolation
Vibration measuring instruments
Energy dissipated in viscous damping
Hysteretic damping
Complex stiffness
Coulomb damping
Measurement of damping
Response to General Dynamic Loading and Transient Response
Introduction
Response to an impulsive force
Response to general dynamic loading
REsponse to a step function load
Response to a ramp function load
Response to a step function load with rise time
Response to shock loading
Response to ground motion
Analysis of response by the phase plane diagram
Analysis of Single-Degree-of-Freedom Systems: Approximate and Numerical Methods
Introduction
Conservation of energy
Application of Rayleigh method to multi-degree-of-freedom systems
Improved Rayleigh method
Selection of an appropriate vibration shape
Systems with distributed mass and stiffness: Analysis of internal forces
Numerical evaluation of Duhamel's integral
Direct integration of the equations of motion
Integration based on piece-wise linear representation of the excitation
Derivation of general formulae
Constant-acceleration method
Newmark's [beta] method
Wilson-[theta] method
Methods based on difference expressions
Errors involved in numerical integration
Stability of the integration method
Selection of a numerical integration method
Selection of time step
Analysis of nonlinear response
Errors involved in numerical integration of nonlinear systems
Analysis of Response in the Frequency Domain
Transform methods of analysis
Fourier series representation of a periodic function
Response to a periodically applied load
Exponential form of fourier series
Complex frequency response function
Fourier integral representation of a nonperiodic load
Response to a nonperiodic load
Convolution integral and convolution theorem
Discrete Fourier transform
Discrete convolution and discrete convolution theorem
Comparison of continuous and discrete Fourier transforms
Application of discrete inverse transform
Comparison between continuous and discrete convolution
Discrete convolution of an infinite- and a finite-duration waveform
Corrective response superposition methods
Exponential window method
The fast Fourier transform
Theoretical background to fast Fourier transform
Computing speed of FFT convolution
Free-Vibration Response: Multi-Degree-of-Freedom Systems
Introduction
Standard eigenvalue problem
Linearized eigenvalue problem and its properties
Expansion theorem
Rayleigh quotient
Solution of the undamped free-vibration problem
Mode superposition analysis of free-vibration response
Solution of the damped free-vibration problem
Additional orthogonality conditions
Damping orthogonality
Numerical Solution of the Eigenproblem
Introduction
Properties of standard eigenvalues and eigenvectors
Transformation of a linearized eigenvalue problem to the standard form
Transformation methods
Iteration methods
Determinant search method
Numerical solution of complex eigenvalue problem
Semi-definite or unrestrained systems
Selection of a method for the determination of eigenvalues
Forced Dynamic Response: Multi-Degree-of-Freedom Systems
Introduction
Normal coordinate transformation
Summary of mode superposition method
Complex frequency response
Vibration absorbers
Effect of support excitation
Forced vibration of unrestrained system
Analysis of Multi-Degree-of-Freedom Systems: Approximate and Numerical Methods
Introduction
Rayleigh-Ritz method
Application of Ritz method to forced vibration response
Direct integration of the equations of motion
Analysis in the frequency domain
Analysis of nonlinear response
Formulation of the Equations of Motion: Continuous Systems
Introduction
Transverse vibrations of a beam
Transverse vibrations of a beam: variational formulation
Effect of damping resistance on transverse vibrations of a beam
Effect of shear deformation and rotatory inertia on the flexural vibrations of a beam
Axial vibrations of a bar
Torsional vibrations of a bar
Transverse vibrations of a string
Transverse vibrations of a shear beam
Transverse vibrations of a beam excited by support motion
Effect of axial force on transverse vibrations of a beam
Continuous Systems: Free Vibration Response
Introduction
Eigenvalue problem for the transverse vibrations of a beam
General eigenvalue problem for a continuous system
Expansion theorem
Frequencies and mode shapes for lateral vibrations of a beam
Effect of shear deformation and rotatory inertia on the frequencies of flexural vibrations
Frequencies and mode shapes for the axial vibrations of a bar
Frequencies and mode shapes for the transverse vibration of a string
Boundary conditions containing the eigenvalue
Free-vibration response of a continuous system
Undamped free transverse vibrations of a beam
Damped free transverse vibrations of a beam
Continuous Systems: Forced-Vibration Response
Introduction
Normal coordinate transformation: general case of an undamped system
Forced lateral vibration of a beam
Transverse vibrations of a beam under traveling load
Forced axial vibrations of a uniform bar
Normal coordinate transformation, damped case
Wave Propagation Analysis
Introduction
The phenomenon of wave propagation
Harmonic waves
One-dimensional wave equation and its solution
Propagation of waves in systems of finite extent
Reflection and refraction of waves at a discontinuity in the system properties
Characteristics of the wave equation
Wave dispersion
Answers to Selected Problems
Index

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